Which two of the calculations give the same answer?
12 ÷ 3
1.4 +2.6
1.4 x 3
2.1+2.4

a.  The iterated integral to evaluate over D is\(\int\limits^{2\pi}_0 \int\limits^{3 cos \theta }_0 \int\limits^{5 r cos \theta}_0 f(r, \theta, z) dz dr dtheta\)

b. The iterated integral to evaluate over D is \(\int\limits^{\pi}_0 \int\limits^{ cos \theta }_{2 cos \theta} \int\limits^{2/3}_0 f(r, \theta, z) dz dr dtheta\)

a) To set up the iterated integral for evaluating over the region D, we first need to determine the limits of integration for each variable. Since D is a right circular cylinder whose base is the circle r = 3cos(theta) and whose top lies in the plane z = 5 - x, we can express the limits of integration as follows:

For theta: 0 to 2π

For r: 0 to 3cos θ

For z: 0 to 5 - rcosθ

Therefore, the iterated integral to evaluate over D is:

\(\int\limits^{2\pi}_0 \int\limits^{3 cos \theta }_0 \int\limits^{5 r cos \theta}_0 f(r, \theta, z) dz dr dtheta\)

b) To set up the iterated integral for evaluating over the region D, we first need to determine the limits of integration for each variable. Since D is a solid right cylinder whose base is the region between the circles r = cos(theta) and r = 2cos(theta) and whose top lies in the plane z = 3y, we can express the limits of integration as follows:

For theta: 0 to π

For r: cosθ to 2cos(θ

For y: 0 to 2/3

Therefore, the iterated integral to evaluate over D is:

\(\int\limits^{\pi}_0 \int\limits^{ cos \theta }_{2 cos \theta} \int\limits^{2/3}_0 f(r, \theta, z) dz dr dtheta\)

Your question is incomplete but most probably your full question is attached below

Learn more about integral at https://brainly.com/question/22850902

#SPJ11

Answer:

2000km=1 hour so 1000km=half an hour (1/2)

5 times half an hour=2.5 hours=2 hours 30 minutes

Answer:144

Step-by-step explanation:

Answer:

D.48

Step-by-step explanation:

Answer:

\( {x}^{2} - 7x = 4\)

\( {x}^{2} - 7x - 4 = 0\)

a = 1, b = -7, c = -4

Answer:

D. \(\sqrt{27}\)

Step-by-step explanation:

A, B, and C are all perfect squares being square rooted. This means that they will all result in whole numbers.

For example: A.   \(\sqrt{9}=3\)

However, D.         \(\sqrt{27}=3\sqrt{3}\), which is not rational because it contains an unsimplifiable square root (sqrt 3)

Answer:

√27

Step-by-step explanation:

√9 = 3

√81 = 9

√36 = 6

√27 = not whole number

Answer:

\(2 {x}^{2} - 8\)

hope it's helpful ❤❤❤

THANK YOU.

Answer:

2x² - 8

Step-by-step explanation:

Given

(x - 2)(2x + 4)

Each term in the second factor is multiplied by each term in the first factor, that is

x(2x + 4) - 2(2x + 4) ← distribute both parenthesis

= 2x² + 4x - 4x - 8 ← collect like terms

= 2x² - 8

Answer:

M(-3, -2.5) and N(3, -1)

Step-by-step explanation:

Given equations:

1st

make x subject

2nd

Substitute equation 1 into 2

x² + xy = 4 + 2y²

\(\sf step : \ x = 4y + 7\)

(4y + 7)² + (4y + 7)y = 4 + 2y²

\(\sf step : \ distribute \ inside \ parenthesis\)

16y² + 56y + 49 + 4y² + 7y = 4 + 2y²

\(\sf step : \ collect \ terms\)

16y² + 4y² -2y² + 56y + 7y + 49 - 4 = 0

\(\sf step : \ simplify\)

18y² + 63y  + 45 = 0

\(\sf step : \ middle \ term \ factor\)

18y² + 18y + 45y + 45 = 0

\(\sf step : \ factor \ out\)

18y(y + 1) + 45(y + 1) = 0

\(\sf step : \ collect \ into \ groups\)

(18y + 45)(y + 1) = 0

\(\sf step : \ set \ to \ zero\)

y = -2.5, -1

Now, find value of x

x = 4y + 7

when y = -2.5, x = 4(-2.5) + 7 = -3

when y = -1, x = 4(-1) + 7 = 3

Hence the coordinates are (x, y) = M(-3, -2.5) and N(3, -1).

Answer:

\(M=\left(-3, -\dfrac{5}{2}\right)\)

\(N=(3,-1)\)

Step-by-step explanation:

Given equations:

\(4y=x-7\)

\(x^2+xy=4+2y^2\)

To find the points of intersection, rearrange the linear equation to isolate x:

\(\implies x=4y+7\)

Substitute the found expression for x into the second equation:

\(\implies (4y+7)^2+(4y+7)y=4+2y^2\)

\(\implies 16y^2+56y+49+4y^2+7y=4+2y^2\)

\(\implies 20y^2+63y+49=4+2y^2\)

\(\implies 18y^2+63y+45=0\)

\(\implies 9(2y^2+7y+5)=0\)

\(\implies 2y^2+7y+5=0\)

Factor the quadratic and solve for y:

\(\implies 2y^2+2y+5y+5=0\)

\(\implies 2y(y+1)+5(y+1)=0\)

\(\implies (2y+5)(y+1)=0\)

\(\implies 2y+5=0 \implies y=-\dfrac{5}{2}\)

\(\implies y+1=0 \implies y=-1\)

Substitute the found values of y into the expression for x and solve for x:

\(\begin{aligned}y=-\dfrac{5}{2} \implies x&=4\left(-\dfrac{5}{2}\right)+7\\x&=-10+7\\x&=-3\end{aligned}\)

\(\begin{aligned}y=-1 \implies x&=4\left(-1\right)+7\\x&=-4+7\\x&=3\end{aligned}\)

Therefore, the coordinates of M and N are:

  \(M=\left(-3, -\dfrac{5}{2}\right)\)  

  \(N=(3,-1)\)

Upper Control Limit for R Chart: UCL = D4 * R-Bar , UCL = 2.114 * 1.000, UCL ≈ 2.115 cm. Therefore, the correct answer is 2.115 cm(d).

To calculate the upper control limit for the R Chart, we need to use the following formula:

Upper Control Limit (UCL) = D4 * R-Bar

Where:

- D4 is a constant value based on the sample size (n=5 in this case).

- R-Bar is the average range of the samples, which is given as 1.000 cm.

The value of D4 for a sample size of 5 is 2.114. (You can find this value in statistical reference tables.)

Now, we can calculate the UCL:

UCL = D4 * R-Bar

   = 2.114 * 1.000

   = 2.114 cm

Rounding to 3 decimal places, the upper control limit for the R Chart is 2.114 cm.

Therefore, the correct option is: d. 2.115 cm

Learn more about average here: https://brainly.com/question/24057012

#SPJ11

The complete question is :

Repeated sampling of a certain process shows the average of all sample ranges to be 1.000 cm. There are 12 random samples and the sample size has been 5. What is the upper control limit for R Chart? Must compute in 3 dec pl. Select one: O a. 2.745 cm O b. 3.005 cm O c. 1.725 cm d. 2.115 cm e. 2.000 cm

L((7,8)) = (-9,23).  To find the value of L((7,8)), we can use the linearity property of the linear operator L.

Since L is a linear operator, we can express any vector in R² as a linear combination of the basis vectors (1,0) and (0,1).

We have L((1,2)) = (-2,3) and L((1,-1)) = (5,2). Therefore, we can express (7,8) as (7,8) = 7(1,2) + 1(1,-1).

Using the linearity property, we can distribute the linear operator L over the linear combination:

L((7,8)) = L(7(1,2) + 1(1,-1))

= 7L((1,2)) + L((1,-1))

= 7(-2,3) + (5,2)

= (-14,21) + (5,2)

= (-9,23)

Know more about linearity property here:

https://brainly.com/question/28709894

#SPJ11

The required value of x is 7.

In the given statement is:

m/HGS = 3x + 5,

m/SGF=21x +3, and m/HGF = 176º.

and, to find the value of 'x'

The two angles, ∠HGS & ∠SGF, when combined, will result in ∠HGF

m ∠HGS = 3x + 5

m ∠SGF = 21x + 3

m ∠HGF = 176°

Set the equation:

m ∠SGF + m ∠HGS = m ∠HGF

Plug in the corresponding terms to the corresponding variables:

21x + 3 + 3x + 5 = 176°

24x + 8 = 176°

24x = 176° - 8

24x = 168°

x = 168°/24

x = 7

Hence, The required value of x is 7.

Learn more about Variables at:

https://brainly.com/question/24357656

#SPJ1

Hey there! I'm happy to help!

In the quadratic formula, the discriminant is square rooted. In this formula you have a ± before this radical. If the discriminant is positive, the solution can be either subtracting or adding the number, so there are 2 real solutions.

If it is 0, subtracting or adding are the same, so there will be just one solution.

You cannot have a negative square root. It is impossible with real numbers, so there are no real solutions.

I hope that this helps! Have a wonderful day! :D

The zeroes based on nature of discriminant is described below.

We know that,

A quadratic equation is of the form ax + bx + c = 0,

Where a, b, and c are constants and x is the variable.

The discriminant of a quadratic equation is given by the expression,

⇒  b² - 4ac.

If the discriminant is positive (b² - 4ac > 0),

Then the quadratic equation has two real solutions.

This is because the quadratic formula, which gives the solutions of the quadratic equation, involves the square root of the discriminant.

Since the discriminant is positive, the square root is a real number, resulting in two distinct real solutions.

If the discriminant is negative (b² - 4ac < 0),

The square root of the discriminant is an imaginary number since it involves a negative integer's square root.

Given that the discriminant is a component of the quadratic formula,

if it is negative, the quadratic formula will include computing the square root of a negative integer, which is not a real number.

This is due to the fact that solving the quadratic equation requires obtaining the square root of the discriminant, and a negative square root is not a real integer.

In conclusion, there are no actual solutions to a quadratic equation with a negative discriminant since the solutions entail calculating the square root of a negative.

When the discriminant is zero,

it means that the quadratic equation has only one solution, which is a real number.

This is because the quadratic formula for finding the solutions of the quadratic equation reduces to a simpler formula when the discriminant is zero. Specifically,

The quadratic formula becomes,

x = -b/2a This formula gives us the only solution of the quadratic equation when the discriminant is zero.

To learn more about quadratic equation visit:

https://brainly.com/question/30098550

#SPJ2

The system of equations has infinite solutions, both equations represent the same line.

Here we have the following system of equations:

-3x+6y=12

2y=x+4

And we want to solve this by substitution, first, we can rewrite the first equation as:

-3x + 3*(2y) = 12

Now we can substitute the second equation 2y = x + 4 in the parenthesis, we will get:

-3x + 3*(x + 4) = 12

Now we can solve this for x.

-3x + 3x + 12 = 12

12 = 12

So this is true for any value of x, which means that both equations represent the same line (thus the system has infinite solutions).

Learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

The number of ways to arrange the school dance committee in a row at a meeting is 3,110,400.

To arrange a school dance committee for a meeting, there are 3 groups of students: freshmen, sophomores and juniors. Each group must sit together by grade and there are 6, 3, and 2 students in each group, respectively.

The two seniors can sit anywhere. Effectively, there are 5 people (3 groups of students and 2 seniors).

Therefore the total number of permutations is the product of these arrangements, which is:

Thus, there are 3,110,400 ways to arrange the school dance committee for the meeting, given the constraints that the freshmen, sophomores, and juniors must sit together by grade & the seniors can sit anywhere.

Learn more about permutation brainly.com/question/28065038

#SPJ4

The answer to following parts are and this can be solved by using probability.

a) 15,890,700 different samples can be chosen

b) 6,523,881 will contain at least one defective chip

c) 41.1%

What is probability?

A probability is the number of desired outcomes divided by the number of total outcomes.

Main body:

The order in which the microchips are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

Cₙ,ₓ is the number of different combinations of x objects from a set of n elements, given by the following formula.

Cₙ,ₓ =\(\frac{ n!}{x!(n-x)!}\)

(a) How many different samples can be chosen?

Samples of 6 from a set of 50.

Then

C₅₀,₆ = \(\frac{50!}{6!(50-6)!}\) =15,890,700

15,890,700 different samples can be chosen

(b) How many samples will contain at least one defective chip?

Either a sample contains no defective chip, or it contains at least one. From a), the sum of them is 15890700.

Then

No defective chips:

Four are defective.

So 50-4 = 46 are not.

This is samples of 6 from a set of 46.

C₄₆,₆ = 46!/6!*40!

9,366,819 samples contain no defective chips.

At least one:

9366819 + n = 15890700

n = 6523881

6,523,881 will contain at least one defective chip

(c) What is the probability (as a percent) that a randomly chosen sample of six contains at least one defective chip

6,523,881 out of 15,890,700

6,523,881/15,890,700 = 0.411

As a percent

41.1%

Hence the answer are as follows.

To learn more about probability click on the link below

https://brainly.com/question/24756209

#SPJ4

Dion's study suffers from selection bias as his sample of individuals on the beach in Miami may not be representative of the entire population's affinity for warm weather.

This is because he is only sampling residents of Miami, Florida, who are on the beach.

This group may not accurately represent the entire population's affinity for warm weather, as it excludes those who may not enjoy the beach or may not have the opportunity to visit the beach.

A more representative sample would include individuals from various locations and backgrounds to better assess the affinity for warm weather across the population.

For similar question on population's.

https://brainly.com/question/29334875

#SPJ11

The person can buy a maximum of three T-shirts to the group of friends.

In this case we have the case of a person that saved some money to go to the State Fair with a group of friends, the maximum number of T-shirts to be bought is derived from the money available after spending to get a ticket to get in to the fair. The number of T-Shirts is found by means of the following operation:

x = ($ 72 - $ 12) / ($ 20)

x = ($ 60) / ($ 20)

x = 3

The person can buy a maximum of three T-shirts for the friends.

To learn more on costs and money: https://brainly.com/question/5997789

#SPJ1

Answer:

x >= 7 OR x < -8

n <= -3 AND n > -6

Step-by-step explanation:

15) 7x - 6 >= 43 OR 10x + 4 < -76

7x >= 43 + 6 OR 10x < -76 - 4

7x >= 49 OR 10x < -80

x >= 7 OR x < -8

you can draw based on this

for >= it is full dot for < it is like circle on the graph

you have to draw both x>= 7 , x < -8 on the same line because it is OR

so both ranges of x are possible

21) 3 + 2n <= -3 AND 1 - 3n < 19

2n <= -3 -3 AND -3n < 19 - 1

2n <= -6 AND -3n < 18

n <= -3 AND 3n > -18

n <= -3 AND n > -6

so it lies between -6 and -3

u can refer pictures below

Answer:

To solve this trigonometric identity, we need to use the definitions of the trigonometric functions and some algebraic manipulation. Here's how we can do it:

cos 14° - sin 14°/ cos 14° + sin 14°

= (cos 14°/cos 14°) - (sin 14°/cos 14°)/(cos 14°/cos 14°) + (sin 14°/cos 14°) (multiplying the numerator and denominator of the second term by cos 14°)

= 1 - tan 14°/1 + tan 14° (using the definitions of cosine and sine, and dividing both terms by cos 14°)

= (1 - tan²14°)/(1 + tan 14°) (using the identity 1 + tan²θ = sec²θ)

= 1/cot 14° - cot 14° (using the definition of cotangent and simplifying the numerator)

= cot 90° - cot 14° (using the identity cot(90° - θ) = tan θ)

= cot (90° + 14°) (using the identity cot(θ + 90°) = -tan θ)

= cot 104°

Since cot(104°) = cot(180° - 76°) = -cot 76°, we can also write the final answer as -cot 76°.

Therefore, the given identity is true, and we have shown that:

cos 14° - sin 14°/ cos 14° + sin 14° = cot 59​ = -cot 76°.

Learn more about Trigonometry Problems here:

https://brainly.com/question/22698523

If there is a zero on the top of the fraction when calculating the slope, then the line is horizontal.

If the numerator (y2 - y1) is zero, it means that the y-coordinates of the two points on the line are the same. This indicates that the line is horizontal, because no matter how far apart the two points are horizontally (i.e., the difference between their x-coordinates), the vertical distance (y2 - y1) between them is zero.

In this case, the denominator (x2 - x1) will be non-zero, because the two points will have different x-coordinates, but since the numerator is zero, the overall fraction will be zero.

So, a zero on the top of the fraction indicates that the line has zero or undefined slope, which happens only for a horizontal or vertical line, respectively. Therefore, if there is a zero on the top of the fraction when calculating the slope, then the line is horizontal.

To know more about slope,

https://brainly.com/question/29082928

#SPJ11

Answer:

x= 25+20y

Step-by-step explanation:

De acuerdo a la situación planteada, la expresión algebraica debe indicar que 25€ que es el valor por la visita más 20€ multiplicado por el número de horas trabajadas es igual al dinero total que se debe pagar. La expresión es:

x= 25+20y, donde

x= valor total a pagar

y= número de horas trabajadas

Answer:

1. 53

2. 20

3. 37

4. 29

Step-by-step explanation:

Since your trying to find the hypotenuse you equation is...

1. 28^2 + 45^2 = C^2

    784 + 2025 = C^2

      Square Root 2809= C^2

    C=53

So after you square root 2809 you get 53.

2. 12^2 + 16^2 = C^2

     144 + 256 = C^2

      Square Root 400 = C^2

    C=20

So after you square root 400 you get 40.

3.  12^2 + 35^2 = C^2

    144 + 1225 = C^2

    Square Root 1369 = C^2

   C=37

So after you square root 1359 you get 37.

4. 20^2 + 21^2 = C^2

   400 + 441 = C^2

  Square root 841 = C^2

  C=20

So after you square root 841 you get 29.

Answer: X^2y + 3xy + 2y -3x^2 -9x -6
explanation

1. Foil (x+2)(x+1)

X^2 +2x + x + 2

2. Simplify

X^2 + 3x + 2

3. Distribute x^2 + 3x +2 (y-3)

X^2y + 3xy + 2y -3x^2 -9x -6

The thermometer is a device that is used to measure the temperature gradient. Anders needs to set the boiling point of water at 100° C.

The thermometer is a device that is used to measure the temperature gradient or the temperature of a body/object.

The boiling point of water is 100°C, therefore, Anders needs to set the boiling point of water at 100° C.

Thus, Anders needs to set the boiling point of water at 100° C.

Learn more about Thermometers:

https://brainly.com/question/24189042

The approximate internal rate of return on this project is approximately 13.59% at which the present value of the cash inflows (profits) is equal to the initial investment.

To calculate the approximate internal rate of return (IRR) for this project, we need to determine the discount rate at which the present value of the cash inflows (profits) is equal to the initial investment.

Given:

Initial investment = $2,000,000

Annual profit generated = $400,000

Number of years = 7

We can set up the following equation:

PV of cash inflows = Initial investment

To calculate the present value of the cash inflows, we need to discount each year's profit at the discount rate (IRR) and sum them up. Using a financial calculator or spreadsheet software, we can iterate different discount rates until the present value of the cash inflows matches the initial investment. Using an iterative process, the approximate internal rate of return (IRR) for this project is found to be approximately 13.59%.

To know more about rate,

https://brainly.com/question/33519589

#SPJ11

Such a number must consist of four 0s and two 1s, with 1 as the leading digit. There 5 choices of places for the remaining 1, so there are only 5 such numbers.

110 000

101 000

100 100

100 010

100 001

The series solution of y" + xy' + y = 0 is y(x) = a_0 [1 - x^2/2! + x^4/4! - x^6/6! + ...] + a_1 [x - x^3/3! + x^5/5! - ...], where a_0 and a_1 are arbitrary constants.

To find the series solution of y" + xy' + y = 0, we can assume a power series solution of the form:

y(x) = ∑(n=0 to ∞) a_n x^n

Taking the first and second derivatives of y(x), we get:

y'(x) = ∑(n=1 to ∞) n a_n x^(n-1)

y''(x) = ∑(n=2 to ∞) n(n-1) a_n x^(n-2)

Substituting these into the differential equation, we get:

∑(n=2 to ∞) n(n-1) a_n x^(n-2) + x∑(n=1 to ∞) n a_n x^(n-1) + ∑(n=0 to ∞) a_n x^n = 0

Simplifying and reindexing the sums, we get:

∑(n=0 to ∞) [(n+2)(n+1)a_(n+2) + (n+1)a_n] x^n = 0

Since this equation must hold for all values of x, each coefficient of x^n must be zero. Therefore, we get the following recurrence relation:

a_(n+2) = -a_n / (n+2)(n+1)

We can use this recurrence relation to find the coefficients of the power series solution. Starting with a_0 and a_1 as arbitrary constants, we can use the recurrence relation to find all other coefficients. For example:

a_2 = -a_0 / 2

a_3 = -a_1 / 6

a_4 = a_0 / (4*3*2)

a_5 = a_1 / (5*4*3)

To know more about arbitrary constants refer here:

https://brainly.com/question/29093928#

#SPJ11

The probability comes out to be 0.2296

We need to calculate the probability of each jet waiting at least 10 minutes before takeoff.

P(X≥10)=?

Let Z be the standard normal variable.

Z=(X-μ)/σ

Where μ is the mean of the taxi and take-off time for commercial jets and σ is the standard deviation of the taxi and takeoff time for commercial jets.

Z=(X-8.3)/2.3

Using the z-score formula, Z=(X-μ)/σ, we can standardize the value of the variable X to get its respective z-score value, z.

With a mean of 8.3 and a standard deviation of 2.3, the standardized score for a taxi and takeoff time of 10 is:

z=(10-8.3)/2.3 = 0.73913

The probability of a jet waiting at least 10 minutes before takeoff can be calculated as follows:

P(X≥10) = P(Z≥0.73913)

The probability of a standard normal random variable z is greater than or equal to 0.73913 is:

1 - Φ(0.73913)

where Φ(z) is the standard normal distribution function.

Using a standard normal distribution table or calculator, we find that:

Φ(0.73913) = 0.7704

Therefore: P(X≥10) = P(Z≥0.73913)= 1 - Φ(0.73913)= 1 - 0.7704= 0.2296

Thus, the probability of each jet waiting at least 10 minutes before takeoff is 0.2296.

Learn more about z-score:

https://brainly.com/question/31871890

#SPJ11

Answer:

x = 6 gallons (of 30% alcohol)

y = 12 gallons (of 60% alcohol)

Step-by-step explanation:

Let

x = liters of 30% alcohol

y = liters of 60% alcohol

There are two unknowns, we need two equations

x + y = 18. (1)

0.30x + 0.60y = 0.50(x+y) (2)

From (1)

x + y = 18

y = 18-x

Substitute the value of y into (2) and solve for x:

0.30x + 0.60y = 0.50(x+y)

0.30x + 0.60(18-x) = 0.50(x+18-x)

0.30x + 10.8 - 0.60x = 0.50(18)

10.8 - 0.30x = 9

-0.30x = -1.8

Divide both sides by -0.30

x = 6 gallons (of 30% alcohol)

Substitute x=6 into (1) and solve for y:

x + y = 18

6 + y = 18

y = 12 gallons (of 60% alcohol)